Difference between revisions of "2011 AMC 12A Problems/Problem 20"
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== Problem == | == Problem == | ||
| + | Let <math>f(x)=ax^2+bx+c</math>, where <math>a</math>, <math>b</math>, and <math>c</math> are integers. Suppose that <math>f(1)=0</math>, <math>50<f(7)<60</math>, <math>70<f(8)<80</math>, <math>5000k<f(100)<5000(k+1)</math> for some integer <math>k</math>. What is <math>k</math>? | ||
| + | |||
| + | <math> | ||
| + | \textbf{(A)}\ 1 \qquad | ||
| + | \textbf{(B)}\ 2 \qquad | ||
| + | \textbf{(C)}\ 3 \qquad | ||
| + | \textbf{(D)}\ 4 \qquad | ||
| + | \textbf{(E)}\ 5 </math> | ||
| + | |||
== Solution == | == Solution == | ||
== See also == | == See also == | ||
{{AMC12 box|year=2011|num-b=19|num-a=21|ab=A}} | {{AMC12 box|year=2011|num-b=19|num-a=21|ab=A}} | ||
Revision as of 02:36, 10 February 2011
Problem
Let 
, where 
, 
, and 
are integers. Suppose that 
, 
, 
, 
for some integer 
. What is ?
Solution
See also
| 2011 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 19 |
Followed by Problem 21 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
